The invention relates to computational fluid dynamics (CFD). More particularly, the invention relates to the design of airfoils for turbomachinery.
Many turbomachines feature sections characterized by alternating circular arrays (often referred to as “rows”) of airfoils. Alternating, oppositely-oriented, rows of rotating blade and fixed vane airfoils may be present in any given section. Performance of the turbomachine is influenced by the size, positioning, and shape of these airfoils. CFD means are commonly used to optimize parameters for desired performance (e.g., efficiency) in desired operating conditions. The behavior of boundary layers, especially on the suction sides of the airfoils, strongly influences airfoil performance. The boundary layer will start as a laminar flow and then typically transition to a turbulent flow. The boundary layer may also separate from the airfoil. The separated boundary layer may then reattach.
Standard practice in the industry is to perform CFD simulations solving the Reynolds Average Navier-Stokes equations with a two-equation turbulence model. The turbulence model is disabled in the laminar portion of the boundary layer. Thus one must know: (a) the location of the boundary between the boundary layer and freestream; and (b) the location on the airfoil at which the boundary layer transitions from laminar to turbulent flow. The former is straightforward and may be done by analyzing the flowfield resulting from a converged CFD solution, which used either fully laminar or fully turbulent models. The latter is more difficult.
It has long been known that freestream turbulence plays a key role in determining the location of the boundary layer transition. A relationship between a critical momentum thickness-based Reynolds number on the one hand and the freestream turbulence intensity and a pressure gradient parameter on the other hand is disclosed in Abu-Ghannam B. J., Shaw R., Natural Transition of Boundary Layers—the Effects of Turbulence, Pressure Gradients and Flow History”, J. Mech. Eng Sci., Vol. 22, pp. 213-228, 1980. A relationship between that critical Reynolds number and the freestream turbulence intensity is disclosed in Mayle, R. E., “The Role of Laminar-Turbulent Transition in Gas Turbine Engines”, ASME Journal of Turbomachinery, Vol. 113, pp. 509-537, 1991.
In addition to modeling transition in attached flow situations, it is advantageous to model transition in separated flow situations. One model for this is disclosed in Roberts, W. B., “Calculation of Laminar Separation Bubbles and Their Effect on Airfoil Performance,” AIAA Journal, Vol. 18, No. 1. pp. 25-31, 1980. The Roberts model relates a momentum thickness-based Reynolds number to the turbulence intensity multiplied by an exponent of the quotient of the chord of the airfoil divided by the turbulence length scale. Nevertheless there is room for further improvement in transition modeling.